We propose that, for the purpose of studying theoretical properties of the knowledge of an agent with Artificial General Intelligence (that is, the knowledge of an AGI), a pragmatic way to define such an agent’s knowledge (restricted to the language of Epistemic Arithmetic, or EA) is as follows. We declare an AGI to know an EA-statement φ if and only if that AGI would include φ in the resulting enumeration if that AGI were commanded: “Enumerate all the EA-sentences which you (...) know.” This definition is non-circular because an AGI, being capable of practical English communication, is capable of understanding the everyday English word “know” independently of how any philosopher formally defines knowledge; we elaborate further on the non-circularity of this circular-looking definition. This elegantly solves the problem that different AGIs may have different internal knowledge definitions and yet we want to study knowledge of AGIs in general, without having to study different AGIs separately just because they have separate internal knowledge definitions. Finally, we suggest how this definition of AGI knowledge can be used as a bridge which could allow the AGI research community to import certain abstract results about mechanical knowing agents from mathematical logic. (shrink)

In 2011, Hibbard suggested an intelligence measure for agents who compete in an adversarial sequence prediction game. We argue that Hibbard’s idea should actually be considered as two separate ideas: first, that the intelligence of such agents can be measured based on the growth rates of the runtimes of the competitors that they defeat; and second, one specific (somewhat arbitrary) method for measuring said growth rates. Whereas Hibbard’s intelligence measure is based on the latter growth-rate-measuring method, we survey other methods (...) for measuring function growth rates, and exhibit the resulting Hibbard-like intelligence measures and taxonomies. Of particular interest, we obtain intelligence taxonomies based on Big-O and Big-Theta notation systems, which taxonomies are novel in that they challenge conventional notions of what an intelligence measure should look like. We discuss how intelligence measurement of sequence predictors can indirectly serve as intelligence measurement for agents with Artificial General Intelligence (AGIs). (shrink)